The following line passes through point $(-5, 1)$ : $y = \dfrac{4}{5} x + b$ What is the value of the $y$ -intercept $b$ ?
Solution: Substituting $(-5, 1)$ into the equation gives: $1 = \dfrac{4}{5} \cdot -5 + b$ $1 = -4 + b$ $b = 1 + 4$ $b = 5$ Plugging in $5$ for $b$, we get $y = \dfrac{4}{5} x + 5$. ${1}$ ${2}$ ${3}$ ${4}$ ${5}$ ${6}$ ${7}$ ${8}$ ${9}$ ${10}$ ${\llap{-}2}$ ${\llap{-}3}$ ${\llap{-}4}$ ${\llap{-}5}$ ${\llap{-}6}$ ${\llap{-}7}$ ${\llap{-}8}$ ${\llap{-}9}$ ${\llap{-}10}$ ${1}$ ${2}$ ${3}$ ${4}$ ${5}$ ${6}$ ${7}$ ${8}$ ${9}$ ${10}$ ${\llap{-}2}$ ${\llap{-}3}$ ${\llap{-}4}$ ${\llap{-}5}$ ${\llap{-}6}$ ${\llap{-}7}$ ${\llap{-}8}$ ${\llap{-}9}$ ${\llap{-}10}$ $(-5, 1)$